The plan says 3/4 inch. Your plywood is 23/32.
That's not a defective sheet. That's Tuesday. And if you cut the dado to 3/4 because that's what the plan said, you now have a joint that's 1/32 loose, visible at the line, and annoying every time you look at it.
Every dimension on a plan is one of two things: a target or a fit. The target is the tabletop width. The apron length. Those come from the design. You aim for them. If you land at 19-15/16 instead of 20 inches, nobody is rebuilding anything. The fit is the dado width, the mortise thickness, the drawer clearance. Those come from the actual part that goes into the actual joint. Get the target wrong by a sixty-fourth and you're fine. Get the fit wrong by a sixty-fourth and you're shimming, filling, or starting over.
The problem is that plans don't distinguish between the two. They just print numbers.
The nominal lie
Lumber dimensions stopped matching reality about a hundred years ago, and we kept the names anyway. A 1×6 is 3/4 by 5-1/2. Hardwood 4/4 stock arrives rough at somewhere between 15/16 and 1-1/16 and mills to 11/16 or 7/8, depending on how much twist you're chasing out and how hungry your planer is.
Sheet goods are more consistent but still dishonest. Hardwood plywood labeled 3/4 typically measures 23/32. Baltic birch runs metric and converts to fractions that don't land on any line your combination square was built for. MDF comes closest to the printed number. "Closest" is doing a lot of work in that sentence.
The plan used nominal dimensions because that's what plans do. It's not wrong. But the gap between the convention and your actual material is yours to close.
The rule
When two parts have to fit each other, measure the actual part before you cut the part that receives it.
Don't set the router table to 3/4 because the plan says 3/4. Measure the plywood. If it's 23/32, cut to 23/32. The dado exists to hold that panel. The panel's actual dimension is the only number that matters.
This applies everywhere. Tenon thickness comes from the mortise, not from the cut list. Drawer box width comes from the measured opening, not from the plan. The rabbet for the back panel matches the actual panel, not the "1/4 inch" the plan specifies.
The plan's number is a starting point. Your material's number is the governing authority. When they disagree, material wins.
The structural exception
There's one category of dimension you don't adjust for material variation: the structural dimension. The dado is cut one-third the thickness of the shelf stock. That ratio comes from physics, not from the plywood's width. You absolutely cut the dado to the actual width of your plywood. But you still respect the one-third depth rule, because the strength of the joint depends on how much material sits below the dado floor.
Mortise depth works the same way. The mortise is 3/8 wide because the tenon is 3/8 (fit dimension, measure the tenon). The mortise is 1-1/2 deep because the joint needs full shoulder contact (structural dimension, don't compromise). When a number has physics behind it, that number doesn't move.
Before you cut
Walk the cut list against your actual stock. Thickness first: what will your boards actually mill to? If the plan calls for 13/16 finished and your 4/4 cherry came in at 13/16 rough, you have a problem before you've made a single cut.
Then find every fit dimension on the plan. Every dado, rabbet, mortise, groove. Write "measure actual" next to each one. Those numbers don't come from the plan. They come from the part in your hands.
The plan is an argument someone made about how a piece of furniture should go together. The board on your bench is evidence. When they disagree, evidence wins.